Math Problem Statement

1. Tentukan titik-titik kritis dari fungsi dan interval berikut ini. 2. Tentukan nilai maksimum dan minimum. 3. Tentukan di mana fungsi monoton naik dan turun. 4. Tentukan fungsi cekung ke atas atau ke bawah. 5. Tentukan titik balik. 6. Uji turunan pertama. 7. Uji turunan kedua.

Solution

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  1. Tentukan titik-titik kritis dari fungsi dan interval berikut ini (Find the critical points for the given functions over specified intervals):

    • For each function f(x)f(x), we need to find the derivative f(x)f'(x), set it to zero, and solve for xx. Critical points occur where f(x)=0f'(x) = 0 or where f(x)f'(x) is undefined within the given interval.
  2. Tentukan nilai maksimum dan minimum (Find maximum and minimum values):

    • Using the critical points found in part 1, along with the endpoints of the interval, we need to evaluate the function at these points to determine the maximum and minimum.
  3. Tentukan dimana fungsi berikut monoton naik dan monoton turun (Determine where

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Math Problem Analysis

Mathematical Concepts

Calculus
Derivative
Critical Points
Maxima and Minima
Monotonic Functions
Concavity
Inflection Points
First Derivative Test
Second Derivative Test

Formulas

f'(x) = 0 for critical points
First derivative test for monotonicity
Second derivative test for concavity

Theorems

Extreme Value Theorem
Mean Value Theorem

Suitable Grade Level

High School (Grades 10-12) or Early College Level